Not knowing too much about the inner workings of these, do I assume
correctly that there is some kind of flow switch inside that fires up the
burner when it detects the cold water tape running? Guessing there is also
thermostat in there somewhere.

Over the past month, it's got steadily worse from whereby messing about
turning the tape on/off got it to fire up to really not working at all.

CH side seems fine.

Any ideas?

Thanks, Rob.